Effect of Acetylene Links on Electronic and Optical Properties of Semiconducting Graphynes

Effect of acetylene links on electronic and optical properties of semiconducting graphynes

Yang Li1†, Junhan Wu1†, Chunmei Li1, Qiang Wang1, 2*, Lei Shen3*

1 School of Materials and Energy, Southwest University, Chongqing, 400715, China 2 Chongqing Key Laboratory for Advanced Materials and Technologies of Clean Energies, Southwest University, Chongqing 400715, P. R. China 3 Department of Mechanic Engineering & Engineering Science, National University of Singapore, Singapore, 117575, Singapore

Abstract: The family of graphynes, novel two-dimensional semiconductors with various and fascinating chemical and physical properties, has attracted great interest from both science and industry. Currently, the focus of graphynes is on graphdiyne, or graphyne-2. In this work, we systematically study the effect of acetylene, i.e., carbon-carbon triple bond, links on the electronic and optical properties of a series of graphynes (graphyne-n, where n = 1-5, the number of acetylene bonds) using the ab initio calculations. We find an even-odd pattern, i.e., n = 1, 3, 5 and n = 2, 4 having different features, which has not be discovered in studying graphyne or graphdyine only. It is found that as the number of acetylene bonds increases, the electron effective mass increases continuously in the low energy range because of the flatter conduction band induced by the longer acetylene links. Meanwhile, longer acetylene links result in larger redshift of the imaginary part of the dielectric function, loss function, and extinction coefficient. In this work, we propose an effective method to tune and manipulate both the electronic and optical properties of graphynes for the applications in optoelectronic devices and photo-chemical catalysis.

Keywords: electronic structure; optical property; sp-sp2 hybridization; graphynes; ab initio calculations

1 Introduction

The large variety of carbon allotropes, showing different physical and chemical properties, is due to the different carbon hybridizations, i.e, sp, sp2, and sp3. For example, the natural three- dimensional (3D) graphite and diamond are formed through sp2 or sp3 hybridizations of carbon atoms, respectively. Meanwhile, the sp2 hybridization occurs in some novel man-made carbon allotropes, such as fullerene [1], carbon nanotube [2] and graphene [3]. In 1987, the concept of sp-sp2 hybridized graphyne-n was theoretically proposed by Baughman[4], where the n indicated the number of carbon- carbon triple (acetylene) bonds in graphyne (see Fig.1). Accordingly, there are several kinds of structures based on the polymerization mode, such as graphyne (n = 1), graphdiyne (n = 2), graphyne- 3 (n = 3) and so on. After the successful synthesis of graphyne (n = 1) in the experiment, graphyne has been of particular interest to its unique semiconducting electronic structure and extensively applications in many fields, such as catalysis, sensor, transistor, energy storage (see reviews [5,6] and references therein). Simultaneously, engineering of tuning the electronic structure by simply constructing the acetylene bonds n has been attracted more and more attention to this kind of 2D materials theoretically and experimentally. Recently, 2D semiconducting graphyne-2 has been synthesized on the copper surface by the cross-coupling reaction [7-9]. Soon, this type of 2D materials attracts great attention in many research fields, such as catalysis, energy storage, water purification, and optoelectronic devices, due to its large interlayer distance, unique porous structure, large specific surface area, and high conductivity [10- 19]. Theoretical calculations reveal that graphyne-2 has higher electron mobility than graphene [20, 21]. Kuang et al., [22] further pointed out that the electron mobility and photoconversion efficiency of perovskite solar cells with graphyne-2 doped was significantly improved, which paves a way for optoelectronic applications of graphyne-2. Wang et al., [17] synthesized graphyne-2 composites by the hydrothermal method, which exhibited excellent photocatalytic degradation of the methylene blue. The π-conjugated structure in graphyne-2 makes it efficient to receive photogenerated electrons in the conduction band, and to suppress the recombination of electrons and holes. Luo et al., [23] found that the multibody effect had a significant impact on the electronic structure and optical absorption

2 of graphyne-2 in both the theory and experiment. Due to the one more acetylene bond in graphyne-2 compared with graphyne-1, the graphyne-2 has larger porous and much softer character than graphyne-1, which indicates that graphdiyne could easily hybrid with other materials for optical application [5, 6]. The difference of the electronic structures and mechanic properties between graphyne and graphdiyne as well as the resulting different potential applications, has been accelerated the engineering and application of the graphyne-n family, especially the properties of graphyne-n with longer acetylene links beyond n = 1 and 2. In this paper, the electronic and optical properties of five members in the graphyne family, i.e., graphyne-n (n = 1-5) are systemically investigated using the ab initio calculations. It was found that the length of the acetylene links will greatly change the feature of the energy bands near the Fermi level. Thus, both the electronic and optical properties of this type of 2D materials could be feasibly tuned and manipulated for optoelectronic devices and photo-chemical catalysis applications. This may open a way for exploring the extended graphynes in optoelectronic applications.

2 Computational Methods

In this work we carried out ab initio calculations with the CASTEP module[24], which was implanted in the framework of the density functional theory (DFT) [25] using the generalized gradient approximation (GGA) in the parameterization of Perdew-Burke-Ernzerhof (PBE) format exchange- correlation functional[26]. The Grimme [27] under dispersion correction (DFT-D) was used to improve the calculation accuracy of the weak interaction in 2D graphynes. The electron-ion interactions were described by the Vanderbilt ultra-soft pseudopotentials (US-PP) [26]. The convergence test and geometric optimization of the graphyne-n unit cell were performed firstly. The kinetic cutoff energy used for plane wave expansions was 650 eV. For graphyne-1, graphyne-2 and graphyne-3, the K point meshes of 11 × 11 × 1 were used in the first Brillouin-zone with the Monkhorst-Pack [28], while for graphyne-4 and graphyne-5 with large unit cells, the Brillouin zone integrations were performed using a Monkhorst–Pack grid of 8 × 8 × 1. The vacuum layer thickness was set to 15 Å to eliminate the interlayer interaction. Each calculation was converged when the total energy changes during the geometry optimization process were less than 1×10-5 eV/atom, and the force per atom and the residual stress of the unit cell was less than 0.01 eV/Å and 0.05 GPa,

3 respectively. The maximum displacement between cycles was less than 0.005 Å when the convergence reached.

3 Results and discussion

3.1 Geometric structures The geometric structures of the unit cells of graphyne-1, graphyne-2, graphyne-3, graphyne-4 and graphyne-5 are shown in Figure 1, respectively. The size of the cavity of graphynes is proportional to the length of the acetylene linkages. The structural stability of graphynes can be estimated by the cohesive energy, which is defined as follows [29] 푛 × 퐸 − 퐸 퐸 = 푎푡표푚 푡표푡 , (1) 푐표ℎ 푛 where Ecoh is the cohesive energy of graphynes, n is the number of carbon atoms in a unit cell, Eatom and Etotal is the energy of a single carbon atom and the total energy in a unit cell, respectively. The details of the lattice constant, cohesive energy and comparison with other reports are shown in Table 1. As can be seen, the calculated lattice parameters in this work are in good agreement with previously reported works. Our cohesive energies are slightly higher than other results, which might be due to the different pseudopotentials used.

Figure 1 The optimized geometric structures of unit cells of 2D graphynes. Each graphyne is named with an index “n” which indicates the number of carbon-carbon triple bonds in a link, highlighted in red, between two adjacent hexagons. (a) Graphyne-1, (b) Graphyne-2, (c) Graphyne-

3, (d) Graphyne-4 and (e) Graphyne-5.

It is noted that the cohesive energy is the energy required for separating the neutral atoms in the ground state at 0 K [30]. Thus, the larger the Ecoh is, the more stable the crystal structure is. According to the calculated cohesive energies in Table 1, it can be found that the planar two-dimensional structure of graphyne-1 is the most stable. Meanwhile, the cohesive energy of graphynes decreases gradually with the increase of the number of acetylene bonds (n).

Table 1 Lattice constants and cohesive energies of graphynes.

Graphyne Graphdiyne Graphyne-3 Graphyne-4 Graphyne-5

Lattice constant This work 6.872 9.436 12.011 14.576 17.592

(Å) Other works 6.86a, 6.877b,6.89c 9.44a, 9.46c,9.490c 12.02a,12.04c,12.43d 14.6a,14.60c -

Cohesive energy This work 8.635 8.513 8.450 8.419 8.397

(eV atom-1) Other works 7.95a,7.21e 7.78a, 7.87e 7.70a 7.66a - a ref. [31]; b ref. [32]; c ref. [33]; d ref. [34]; e ref. [29]

3.2 Electronic properties

(a) (b) (c) (d) (e) Graphyne Graphdiyne 6 Graphyne-3 Graphyne-4 Graphyne-5

4 B

B 2 B B A A A A A

0 Eg=0.446eV Eg=0.464eV Eg=0.548eV Eg=0.524eV Eg=0.544eV

Energy/eV -2

-4

-6  M K   M K   M K   M K   M K 

Figure 2 The energy band structures of graphyne-n. Eg is the direct bandgap. A and B indicate the possible electron 5 excitation, hopping from the valence band to conduction band.

Figure 2 shows the band structures of graphynes. It can be seen that all of them are direct bandgap (Eg) semiconductors with a bandgap of 0.446, 0.464, 0.548, 0.524 and 0.544 eV, respectively. It is worth noting that the bandgap size is not simply linearly proportional to the number of acetylene bonds (n). Interestingly, the position of the direct bandgap of graphyne-n with odd n, i.e., n = 1, 3, 5, is located at the M-point, while it is at the -point for even n. Meanwhile, the energy-band dispersions at the bottom of the conduction band and the top of valence band are quite similar for all graphynes, which indicates that they have similar effective mass of both electrons and holes. The effective mass of electrons and holes in semiconductors is an essential parameter, which greatly affect the performance of electronic and/or optical devices. The effective mass of graphynes is calculated by the following equation [35]

1 1 휕2퐸(푘) = . (2) 푚∗ ℏ2 휕푘2

The effective mass in the conduction band (mc, holes) and valence band (mv, electrons) is listed in Table 2. It is found that the effective mass is isotropic from M to K and Γ for graphyne-n with the even (n = 2, 4) acetylene bonds, while it is anisotropic if n is odd. Our calculations show that the low energy levels of the conduction band are mainly contributed by the 2p state of carbon atoms, where the electrons have a quite small effective mass under the excitation of photons. This indicates that it facilitates the formation of the effective photogenerated electrons and the transferred charge carriers, while more effective photogenerated holes would take place in the valence-band region.

Table 2 The effective mass of graphynes in the conduction (mc) and valence band (mv), and band gap (Eg).

Structure mc/m0 mv/m0 Eg (eV)

→ ← → ←

Graphyne-1 0.146(0.15a,0.21b) 0.086(0.063a,0.087b) 0.150(0.17a,0.22b) 0.068(0.066a,0.0901b) 0.446 at M (0.46c,0.47d,e)

Graphyne-2 0.080(0.073a) 0.074(0.075a) 0.464 at  (c,0.46f,h)

Graphyne-3 0.082(0.099a ) 0.053(0.081a ) 0.106(0.12a ) 0.081(0.085a ) 0.548 at M (0.56d)

Graphyne-4 0.078(0.081a) 0.110(0.080a) 0.524 at  (d)

Graphyne-5 0.101 0.091 0.133 0.120 0.544 at M

6 a: ref. [31]; b: ref. [32]; c: ref. [33]; d: ref. [36]; e: ref. [37]; f: ref. [38]; h: ref. [39]

It is found that all graphynes have covalent bonds from the Mulliken population (MP) analysis (Table S1), implying a good structural stability of graphynes. Moreover, the MP analysis shows that the electronic states of graphynes are mainly contributed by the C-2p state, which is consistent with

2 2 the PDOS analysis in Figure S1. The bond lengths and band populations of C1-C2 (sp -sp ), C2-C3

2 (sp -sp), C4-C5 (sp-sp) and C6-C7 (sp-sp) bonds of graphynes (see in Figure 1) remain constant with the increase of the number of acetylene bonds (n). While the bond lengths (band populations) of C3-

C4, C5-C6 and C7-C8 (sp≡sp) bonds (Figure 1) are enlarged as n increases. These alternate bonding characteristics are also illustrated by the charge-density-difference calculations as shown in Figure S2. Such alternate -C≡C-C≡C- structure can energetically stabilize atomic carbon chains or rings which have been reported in many carbon allotropes [40, 41].

3.3 Optical Properties

The calculated band structures of graphynes in Figure 2 show that they all are direct band-gap semiconductors, and the values of band gap are close to that of silicon (0.57 eV GGA-PBE[42]). Thus, we next study the optical properties of graphynes and their potential optoelectronic applications. It is well-known that standard GGA functionals like PBE underestimate the band gap. One of major improvements in the band-gap calculation is to use the hybrid functionals, such as HSE06 [43]. However, both GGA-PBE and HSE06 give similar spectra except for an energy shift of graphynes [44], so only GGA-PBE results are presented in this work. The complex dielectric function ε(ω), a significant parameter to determine the polarization effect inside materials, is calculated as:

ε(ω) = 휀1(휔) + 𝑖휀2(휔), (3) where the imaginary part of the dielectric function ε2(ω) describes the absorption of light, the real part of the dielectric function ε1(ω) represents the amplitude modulation that’s the resonant absorption of the electron transition [45]. (4) 2 2 | ( )|2 3 8휋 푒 3 2 푒 ∙ 푀퐶푉 퐾 ℏ 휀1(휔) = 1 + 2 ∙ ∑ ∫ 푑 푘 × 2 2 2 푚 2휋 [퐸퐶(퐾) − 퐸푉(퐾)] [퐸퐶(퐾) − 퐸푉(퐾)] − ℏ 휔 푉,퐶 퐵푍 (5)

4휋2 2 휀 (휔) = ∙ ∑ ∫ 푑3푘 |푒 ∙ 푀 (푘)|2 × 훿[퐸 (퐾) − 퐸 (퐾) − ℏ휔] 2 푚2휔2 2휋 푒푣 퐶 푉 푉,퐶 퐵푍

1/2 2 2 훪(휔) = √2휔 [√휀1(휔) − 휀2(휔) ] (6)

휔 ω 휔 휎(휔) = 휀 (ω) + 𝑖 [ − 휀 (ω)] 4휋 2 4휋 4휋 1 (7)

(푛 − 1)2 − 푘2 푛(휔) = (8) (푛 + 1)2 + 푘2

휀2(휔) (휔) = 2 2 (9) 휀1(휔) + 휀2(휔)

2 √휔−1 R(ω) = | | , (10) √휔+1

where m is the free electron mass, e the free electric charge, ω the incident photon frequency, BZ the first Brillouin zone, |e﹒MCV(K)| the momentum transition matrix element, K the inverted lattice vector, k the extinction coefficient, C the conduction band, V the valence band, EC(K) and EV(K) the intrinsic level of the conduction and valence bands. Meanwhile, the absorption coefficient I(ω), conductivity σ(ω), refractive index n(ω), loss function L(ω) and reflectivity R(ω) can all be deduced from ε(ω) with the Kramers-Kronig dispersion [46-48].

6 Graphyne Graphyne (a) A Graphdiyne (b) 12 Graphdiyne A Graphyne-3 Graphyne-3 5 A A Graphyne-4 Graphyne-4 Graphyne-5 Graphyne-5

A 6 9

4 4 Visible light Visible B 5 light Visible 3

3 4 6 2

B 3 0 2 B 2 3 -1 1

-2

1 2 3 4 5 6 function Re Dielectric Im Dielectric function Im Dielectric 1 1 2 3 4 5 6 7 8 9 10

0 0

Graphyne Graphyne (c) 10 Graphdiyne (d) Graphdiyne Graphyne-3 1.2 Graphyne-3 Graphyne-4 Graphyne-4 8 Graphyne-5 Graphyne-5 1.5 -1 8

1.2 cm 4 6 6 0.8

0.9

4 0.6 4 2 0.3

0.4 0.0

1 2 3 4 5 6 7 1 2 3 4 5 6 7 Conductivity(1/fs)

Absorption/10 2

0 0.0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Energy (eV) Energy (eV) Figure 3 (a) The imaginary and (b) real parts of complex dielectric function of graphynes. (c) The absorption function and (d) electrical conductivity of graphynes. The visible light region is labeled by two vertical dotted lines. The low-energy part is enlarged in the insets.

Figure 3 shows the calculated imaginary and real parts of complex dielectric function, absorption function and electrical conductivity of graphynes. The peak position of ε2(ω) is determined by the band gap and the degree of non-localization in the low energy regions. With the increase of the number of acetylene bonds, ε2(ω) of graphynes has redshift as shown in Figure 3a. For the real part of the dielectric function ε1(ω), the static dielectric constant (capacitance) is denoted as ε1(0) at the zero frequency. The ε1(0) of graphynes is strongly dependent to the corresponding band gaps as shown in Table 3. Our results in Figure 3b show that ε1(ω) dramatically decays to zero with the increase of the photon energies, indicating a resonance of the energy transition between electron and photon in graphynes. Figure 3b shows that ε1(ω) of graphyne-2,3,4,5 has negative values (positive for graphyne-1). According to the wave vector equation bellow:

2 2 휔 휀1 = 푐 (휥 · 푲), (11)

ε1<0 means that the wave vector K is an imaginary number. Furthermore, this negative value region is redshift with the increase of the number of acetylene bonds (n) as shown in Figure3b. 9

Figure 3c shows that the absorption coefficient in graphynes increases first and consequently decreases as the photon energy goes up. The peak of the absorption coefficient of graphynes shifts to the low energy region and induces a narrow absorption range. Further analysis on the absorption function of graphyne-1 (Figure 3c) shows that there are four main absorption peaks at 1.95, 2.96, 6.63 and 12.03 eV, which are well consistent with the experimental values [23]. For graphyne-2 and graphyne-3, the highest peak is located within the ultraviolet region. Thus, they probably may have the applications in ultraviolet protection or detection materials. The shift of the photoconductivity of graphynes with the photon energy is shown in Figure 3d. The conductivity peaks of graphyne-1 are at 1.46, 2.59, 6.24 and 11.97 eV, respectively. The profiles of the photoconductivity of graphynes shift to the low-energy region (Figure 3d), which is approaching to the energy rage of the visible light.

The peak energy of the dielectric function ε2(ω), energy of electron interband transition, static dielectric constant ε1(0) and absorption edges are presented in Table 3. For graphyne-1, the primary peaks of ε2(ω) are located at A (0.9 eV) and B (6.1 eV). Based on the band structure in Figure 2, the peak A is mainly caused by the transition between the unoccupied states at 0.70 eV and the occupied states at -0.20 eV. Meanwhile, the peak B primarily originates from the transition from -2.07 eV to 4.03 eV of the 2p electrons in the valence band of the C atoms. The details of transition of two peaks in ε2(ω) of graphyne-2, graphyne-3 and graphyne-4 are summarized in Table 3. For graphyne-5, it is worth noting that the imaginary part of the dielectric function ε2(ω) gives rise to the bimodal which shows just only one peak at 1.1 eV due to the band localization and redshift of the function profile (see in Figure 3). Furthermore, the transition between the occupied state at -0.25 eV and the empty state at 0.85 eV corresponds to the peak A. Notice that the peak in the imaginary part of the dielectric function ε2(ω) may not correspond to a single inter-band transition (Figure 2), other inter-band transitions at the same peak energy may also be possible to occur in the band structure [49, 50].

Table 3 The energy corresponding to the peak of the imaginary part of the dielectric function ε2(ω), energy of electron inter-band transition, static dielectric constant ε1(0) and absorption edges Eop of graphynes.

Structure Photon energy (eV) Transition(eV) ε1(0) Eop (eV)

A=0.9 -0.20→0.70 Graphyne 12.9 5.37 B=6.1 -2.07→4.03

A=1.2 -0.36→0.84 Graphdiyne 10.3 3.57 B=4.1 -2.64→1.46

A=1.0 -0.21→0.79 Graphyne-3 8.9 2.65 B=3.0 -1.10→1.90

A=1.1 -0.27→0.84 Graphyne-4 9.6 2.15 B=2.4 -0.80→1.60

Graphyne-5 A=1.1 -0.25→0.85 8.9 1.79

24 Graphyne 21 Graphdiyne Graphyne-3 18 Graphyne-4 ) Graphyne-5 15

eV/cm 12

( 2

) 9  0 1 2 3 4 5 6

ah ( 6

0 0.0 1.5 3.0 4.5 6.0 7.5 9.0 Energy (eV)

Figure 4 Optical absorption edges of graphynes, which are enlarged in the inset.

The optical absorption edges of graphynes are shown in Figure 4. The optical absorption band edge Eop is described by the following extrapolation relationship [51]:

푛 훼ℎ휈 = 퐴(ℎ휈 − 퐸표푝) , (12) where α represents the absorption spectrum, ℎ휈 is the photon energy, A is a function of the refractive index of the material, the reduced mass and the speed of light in vacuum. For direct bandgap semiconductors, n takes 0.5. The calculated values of the optical absorption band edge in graphyne-n are listed in Table 3. It is found that the absorption band edge shifts to the low energy region with the increase of n. Moreover, there is a deviation between the absorption band edge and the corresponding band gap. It is mainly due to the electron localization in the free energy level of band structures.

5 2.0 Graphyne Graphyne Graphdiyne (a) Graphdiyne (b) Graphyne-3 Graphyne-3 4 Graphyne-4 Graphyne-4 1.5 Graphyne-5 Graphyne-5

2.5 1.5 Visible light Visible 3 2.0 light Visible 1.0

1.5 1.0

1.0 2 0.5

0.5

0.0 0.5 0.0 Re Refractive index Re Refractive 1 2 3 4 5 6 7 8 9 10 index Im Refractive 0 1 2 3 4 5 6 7 8

0 0.0 Graphyne Graphyne (c) Graphdiyne (d) 0.8 Graphdiyne 12 Graphyne-3 Graphyne-3 Graphyne-4 Graphyne-4 Graphyne-5 Graphyne-5

9 0.6

6 0.4

Reflectivity Loss function

3 0.2

0 0.0 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20

Energy (eV) Energy (eV)

Figure 5 (a) The real and (b) imaginary parts of complex refractive index of graphynes. (c) The loss function and (d) reflectivity of graphynes. The visible light region is labeled by two vertical dotted lines. The low- energy part is enlarged in the insets of (a) and (b).

The relationship between the complex refractive index n(ω) and extinction coefficient k(ω) with the photon energy of graphynes is shown in Figs. 5a and 5b. At the frequency of zero, the static refractive index of graphyne-n (n = 1-5) are located at 3.61, 3.22, 3.00, 3.01 and 2.99 eV, respectively. This indicates that the static index of the refraction strongly depends on the band gap of graphynes. Furthermore, the complex refractive index of graphynes goes down first, and then raises up with the increase of the photon energy. The graphynes have distinct peaks of the energy loss in the calculated 12 profile as shown in Figure 5c. They correspond to the region of ε1(ω)=0 and ε2(ω)<0, which are the resonance peaks of the energy loss function in graphynes. The reflection spectrum of graphynes is shown in Figure 5d. Our results show that the reflectivity R(0) of graphyne-1 is approaching to 32.2, and diminishes with the increase of the photon energy. The maximum value is 12.4 % at the photon energy of 7.20 eV. Furthermore, as the acetylene bonds (n) increase, the profiles of the energy loss function shift to the low-energy region, and the electron localization and maximum value is enhanced (Figure S3).

4 Conclusions

In summary, we carried out ab initio studies on the geometric, electronic and optical properties of 2D graphyne-n sheets, a family of sp-sp2 hybrid materials with acetylene bonds. The odd-even pattern of n of graphynes on the position of direct band gaps and the dispersion of the effective mass is revealed by the electronic-structure calculation. Our photoelectron transport results show a redshift of the imaginary part of the dielectric function with the increase of the number of acetylene bonds. Furthermore, the loss function and extinction coefficient moves to the low-energy region with the increase of n. These findings show that the optical parameters could be tuned and manipulated by the number of acetylene bonds to fulfill different applications.

Acknowledgments: This work was financially supported by by the Sumin Zeng project in Southwest University (ZSM2021008), the Fundamental Research Funds for the Central Universities

(XDJK2017B043), and Singapore MOE Tier 1 grant (R- 265-000-691-114).

Data Availability: The data that support the findings of this study are available from the corresponding author upon reasonable request.

*Corresponding author [email protected] (Qiang Wang)

* Corresponding author [email protected] (Lei Shen)

Supporting Information Supporting Information is available free of charge via the Internet at http://pubs.acs.org or from the author. Authors Information Corresponding Authors: Qiang Wang - School of Materials and Energy and Chongqing Key Laboratory for Advanced Materials and Technologies of Clean Energies, Southwest University, Chongqing 400715, P. R. China; Email: [email protected] Lei Shen - Department of Mechanic Engineering & Engineering Science, National University of

Singapore, Singapore, 117575, Singapore; Email: [email protected] Authors: Yang Li - School of Materials and Energy, Southwest University, Chongqing, 400715, China Junhan Wu - School of Materials and Energy, Southwest University, Chongqing, 400715, China Chunmei Li - School of Materials and Energy, Southwest University, Chongqing, 400715, China †these authors are equal contribution to this work.

References:

[1] Krätschmer W.; Lamb Lowell D.; Fostiropoulos K.; Huffman Donald R.. Solid C60: a new form of carbon. Nature 1990, 347, 354-358.

[2] Iijima, S. Helical microtubules of graphitic carbon. Nature 1991, 354, 56–58.

[3] Novoselov K. S.; Geim A. K.; Morozov S. V.; Jiang D.; Zhang Y.; Dubonos S. V.; Grigorieva I. V.; Firsov A. A. Electric Field Effect in Atomically Thin

Carbon Films. Science 2004, 36, 666-669.

[4] Baughman R. H.; Eckhardt H..Structure-property predictions for new planar forms of carbon: Layered phases containing Sp2 and sp atoms. J. Chem. Phys.

1987, 87, 6687-6699.

[5] Yongjun Li, Liang Xu, Huibiao Liu and Yuliang Li. Graphdiyne and graphyne: from theoretical predictions to practical construction. Chemical Society

Review 2014, 43, 2572.

[6] Qing Peng, Albert K Dearden, Jared Crean, Liang Han, Sheng Liu, Xiaodong Wen, Suvranu De. New materials graphyne, graphdiyne, graphone, and graphane: review of properties, synthesis, and application in nanotechnology. Nanotechnology, Science and Applications 2014, 7, 1-29.

[7] Li G. X.; Li Y. L.; Liu H. B.; Guo Y. B.; Li Y. J.; Zhu D. B.. Architecture of graphdiyne nanoscale films. Chemical Communication 2010, 46, 3256-3258.

[8] Shang H,; Zou Z.; Li L.; Wang F.; Liu H. B.; Li Y. J.; Li Y. L.. Ultrathin Graphdiyne Nanosheets Grown In Situ on Copper Nanowires and Their Performance as Lithium‐Ion Battery Anodes. Angewandte Chemie 2018, 57, 774-778.

[9] Zhou W. X.; Shen H.; Wu C.; Tu Z.; He F.; Gu Y.; Xue Y.; Zhao Y.; Yi Y.; Li Y.; Li Y.. Direct Synthesis of Crystalline Graphdiyne Analogue Based on

Supramolecular Interactions. Journal of the American Chemical Society 2019, 1, 48-52.

[10] Han Y. Y.; Lu X. L.; Tang S. F.; Yin X. P.; Wei Z. W.; Lu T. B.. Metal‐Free 2D/2D Heterojunction of Graphitic Carbon Nitride/Graphdiyne for Improving the

Hole Mobility of Graphitic Carbon Nitride. Advanced Energy Materials 2018, 8, 1702992-1702999.

[11] He J.; Bao K.; Cui W.; Yu J.; Huang C.; Shen X.; Cui Z.; Wang N.. Construction of Large‐Area Uniform Graphdiyne Film for High‐Performance Lithium‐

Ion Batteries. Chemistry A European Journal 2018, 24, 1187-1192.

[12] Liu R.; Liu H.; Li Y.; Yi Y.; Shang X.; Zhang S.; Yu X.; Zhang S.; Cao H.; Zhang G.. Nitrogen-doped graphdiyne as a metal-free catalyst for high-performance oxygen reduction reactions. Nanoscale 2014, 6, 11336-11343.

[13] Liu R.; Zhou J.; Gao X.; Li J.; Xie Z.; Li Z.; Zhang S.; Tong L.; Zhang J.; Liu Z.. Graphdiyne Filter for Decontaminating Lead‐Ion‐Polluted Water. Advanced

Electronic Materials 2017, 3, 1700122.

[14] Parvin N.; Jin Q.; Wei Y.; Yu R.; Zheng B.; Huang L.; Zhang Y.; Wang L.; Zhang H.; Gao M.; et al. Few‐Layer Graphdiyne Nanosheets Applied for

Multiplexed Real‐Time DNA Detection. Advanced Materials 2017, 29, 1606755.

[15] Wang S.; Yi L.; Halpert J. E.; Lai X.; Liu Y.; Cao H.; Yu R.; Wang D.; Li Y.. A Novel and Highly Efficient Photocatalyst Based on P25–Graphdiyne

Nanocomposite. Small 2012, 8, 265-271.

[16] Xue Y.; Zou Z.; Li Y.; Liu H.; Li Y.; Graphdiyne‐Supported NiCo2S4 Nanowires: A Highly Active and Stable 3D Bifunctional Electrode Material. Small

2017, 13, 1700936.

[17] Zhang H.; Xia Y.; Bu H.; Wang X.; Zhang M.; Lou Y.; Zhao M.. Graphdiyne: A promising anode material for lithium ion batteries with high capacity and rate capability. Journal of Applied Physics 2013, 113, 044309.

[18] Zhang S.; Liu H.; Huang C.; Cui G.; Li Y.. Bulk graphdiyne powder applied for highly efficient lithium storage. Chem. Commun. 2015, 51, 1834-1837.

[19] Zou Z.; Shang H.; Chen Y.; Li J.; Liu H.; Li Y.; Li Y.. A facile approach for graphdiyne preparation under atmosphere for an advanced battery anode. Chem.

Commun. 2017, 53, 8074-8077.

[20] Padilha J. E.; Fazzio A.; Silva A. J. R.. Directional Control of the Electronic and Transport Properties of Graphynes. The Journal of Physical Chemistry C

2014, 118, 18793-18798.

[21] Chen J.; Xi J.; Wang D.; Shuai Z.. Carrier Mobility in Graphyne Should Be Even Larger than That in Graphene: A Theoretical Prediction. The Journal of

Physical Chemistry Letters 2013, 4, 1443-1448.

[22] Kuang C.; Tang G.; Jiu T.; Yang H.; Liu H.; Li B.; Luo W.; Luo W.; Li X.; Zhang W.; Lu F.; et al. Highly Efficient Electron Transport Obtained by Doping

PCBM with Graphdiyne in Planar-Heterojunction Perovskite Solar Cells. Nano Letters 2015, 15, 2756-2762.

[23] Luo G.; Qian X.; Liu H.; Qin R.; Zhou J.; Li L.; Gao Z.; Wang E.; Mei W. N.; Lu J.; et al.. Quasiparticle energies and excitonic effects of the two-dimensional carbon allotrope graphdiyne: Theory and experiment. Physical Review B 2011, 84, 075439.

[24] Perdew J. P.; Burke K.; Ernzerhof M.. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78, 1396. 15

[25] Segall M. D.; Lindan P. J. D.; Probert M.; Pickard C. J.; Hasnip P. J.; Clark S. J.; Payne M. C.. First-principles simulation: ideas, illustrations and the CASTEP code. Journal of Physics: Condensed Matter 2002, 14, 2717.

[26] Vanderbilt D.. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Physical Review B 1990, 41, 7892.

[27] Grimme S.; Antony J.; Ehrlich S.; Krieg H.. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the

94 elements H-Pu. The Journal of Chemical Physics 2010, 132, 154104.

[28] Chadi D.J.. Special points for Brillouin-zone integrations. Physical Review B 1977, 16, 1746.

[29] Puigdollers A. R.; Alonso G.; Gamallo P.. First-principles study of structural, elastic and electronic properties of α-, β- and γ-graphyne. Carbon 2016, 96,

879-887.

[30] Dickman S., Senozan N. M.; Hunt R. L.. Thermodynamic Properties and the Cohesive Energy of Calcium Ammoniate. The Journal of Chemical Physics

1970, 52, 2657-2663.

[31] Ducéré, J.M.; C. Lepetit C.; Chauvin R.. Carbo-graphite: Structural, Mechanical, and Electronic Properties. The Journal of Physical Chemistry C 2013, 117,

21671-21681.

[32] Naritta N.; Nagai S.; Suzuki S.; Nakao K.. Optimized geometries and electronic structures of graphyne and its family. Physical Review B 1998, 58, 11009.

[33] Yue Q.; Chang S.; Kang J.; Qin S.; Li J.. Mechanical and Electronic Properties of Graphyne and Its Family under Elastic Strain: Theoretical Predictions. The

Journal of Physical Chemistry C 2013, 117, 14804-14811.

[34] Cranford S. W.; Brommer D. B.; Buehler M.. Extended graphynes: simple scaling laws for stiffness, strength and fracture. Nanoscale, 2012, 4, 7797-7809.

[35] Harald I.; Hans L.; Laszlo M.; David M.. Solid-State Physics: An Introduction to Theory and Experiment. American Journal of Physics 1992, 60, 1053-1054.

[36] Srinivasu K.; Ghosh S. K.. Graphyne and Graphdiyne: Promising Materials for Nanoelectronics and Energy Storage Applications. The Journal of Physical

Chemistry C 2012, 116, 5951-5956.

[37] Zhou J.; Lv K.; Wang Q.; Chen X. S.; Sun Q.; Jena P.. Electronic structures and bonding of graphyne sheet and its BN analog. The Journal of Chemical

Physics 2011, 134, 174701.

[38] Long M.; Tang L.; Wang D.; Li Y.; Shuai Z.. Electronic Structure and Carrier Mobility in Graphdiyne Sheet and Nanoribbons: Theoretical Predictions. ACS

Nano 2011, 5, 2593-2600.

[39] Zheng Q.; Luo G.; Liu Q.; Quhe R.; Zheng J.; Tang K.; Gao Z.; Nagase S.; Lu J.. Structural and electronic properties of bilayer and trilayer graphdiyne.

Nanoscale 2012, 4, 3990-3996.

[40] Shen L.; Zeng M.; Yang S. W.; Zhang C.; Wang X.; Feng Y.. Electron Transport Properties of Atomic Carbon Nanowires between Graphene Electrodes.

Journal of the American Chemical Society 2010, 132, 11481-11486.

[41] Zhang L.; Li H.; Feng Y. P.; Shen L.. Diverse Transport Behaviors in Cyclo[18]carbon-Based Molecular Devices. The Journal of Physical Chemistry Letters

2020, 11, 2611-2617.

[42] Tran F.; Blaha P.. Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory. The Journal of Physical

Chemistry A 2017, 121, 3318-3325.

[43] Deák P.; Aradi B.; Frauenheim T.; Janzén E.; Gali A.. Accurate defect levels obtained from the HSE06 range-separated hybrid functional. Physical Review

B 2010, 81, 153203.

[44] Kang J.; Li J.; Wu F.; Li S. S.; Xia J. B.. Elastic, Electronic, and Optical Properties of Two-Dimensional Graphyne Sheet. The Journal of Physical Chemistry

C 2011, 115, 20466-20470.

[45] Okoye C. M. I.. Theoretical study of the electronic structure, chemical bonding and optical properties of KNbO3 in the paraelectric cubic phase. Journal of

Physics: Condensed Matter 2003, 15, 5945.

[46] Kronig R. D. L.. On the Theory of Dispersion of X-Rays. Journal of the Optical Society of America 1926, 12, 547-557.

[47] Xie Z.; Hui L.; Wang J.; Zhu G.; Chen Z.; Li C.. Electronic and optical properties of monolayer black phosphorus induced by bi-axial strain. Computational

Materials Science 2018, 144, 304-314.

[48] Zheng S.; Wu E.; Feng Z.; Zhang R.; Xie Yuan.; Yu Y.; Zhang R.; Li Q.; Liu J.; Pang W.; et al.. Acoustically enhanced photodetection by a black phosphorus–

MoS2 van der Waals heterojunction p–n diode. Nanoscale 2018, 10, 10148-10153.

[49] Almeida J. S.; Ahuja R.. Tuning the structural, electronic, and optical properties of BexZn1−xTe alloys. Applied Physics Letters 2006, 89, 061913.

[50] Ma T. H.; Yang C. H.; Xie Y.; Sun L.; Lv W. Q.; Wang R.; Zhu C. Q.; Wang M.. Electronic and optical properties of orthorhombic LiInS2 and LiInSe2: A density functional theory investigation. Computational Materials Science 2009, 47, 99-105. 16

[51] Srikant V. Clarke D. R.. Optical absorption edge of ZnO thin films: The effect of substrate. Journal of Applied Physics 1997, 81, 6357.

Abstract Graphics